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Article

S. Askari, M.H. Shojaeefard and K. Goudarzi

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and…

Abstract

Purpose

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and three analytical models including shock and expansion wave theory, Busemann's second‐order linearized approximation and characteristic method (CHM).

Design/methodology/approach

Flow over double‐wedge and biconvex airfoils was investigated by the CFD technique using the Spalart‐Allmaras turbulence model for computation of the Reynolds stresses. Flow was considered compressible, two dimensional and steady. The no slip condition was applied at walls and the Sutherland law was used to calculate molecular viscosity as a function of static temperature. First‐order upwind discretization scheme was used for the convection terms. Finite‐volume method was used for the entire solution domain meshed by quadratic computational cells. Busemann's theory, shock and expansion wave technique and CHM were the analytical methods used in this work.

Findings

Static pressure, static temperature and aerodynamic coefficients of the airfoils were calculated at various angles of attack. In addition, aerodynamic coefficients of the double‐wedge airfoil were obtained at various free stream Mach numbers and thickness ratios of the airfoil. Static pressure and aerodynamic coefficients obtained from the analytical and numerical methods were in excellent agreement with average error of 1.62 percent. Variation of the static pressure normal to the walls was negligible in the numerical simulation as well as the analytical solutions. Analytical static temperature far from the walls was consistent with the numerical values with average error of 3.40 percent. However, it was not comparable to the numerical temperature at the solid walls. Therefore, analytical solutions give accurate prediction of the static pressure and the aerodynamic coefficients, however, for the static temperature; they are only reliable far from the solid surfaces. Accuracy of the analytical aerodynamic coefficients is because of accurate prediction of the static pressure which is not considerably influenced by the boundary layer. Discrepancies between analytical and numerical temperatures near the walls are because of dependency of temperature on the boundary layer and viscous heating. Low‐speed flow near walls causes transformation of the kinetic energy of the free stream into enthalpy that leads to high temperature on the solid walls; which is neglected in the analytical solutions.

Originality/value

This paper is useful for researchers in the area of external compressible flows. This work is original.

Details

Engineering Computations, vol. 28 no. 4
Type: Research Article
ISSN: 0264-4401

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Article

Yazhou Mao, Yang Jianxi, Jinchen Ji, Wenjing Xu and Quanyuan Guo

Currently, there is a lack of fast and highly accurate on analytical solution of Reynolds equation for evaluating the characteristics of surface textured bearing. This…

Abstract

Purpose

Currently, there is a lack of fast and highly accurate on analytical solution of Reynolds equation for evaluating the characteristics of surface textured bearing. This paper aims to develop such an analytical solution of Reynolds equation for an effective analysis of the characteristics of surface textured bearings.

Design/methodology/approach

By using the separation of variables method and mean eigenvalue method, the analytical solution is constructed. The CFD simulations and experimental results are used to validate the correctness of the analytical solution.

Findings

The analytical solution can accurately evaluate the characteristics of textured bearings. It is found that the larger the eccentricity ratio and aspect ratio, the greater the oil film force. It also found that the smaller the eccentricity ratio, the larger the Sommerfeld number S. When eccentricity ratio e = 0.65, the attitude angles of different oil boundaries are same. The effect of different aspect ratios on dynamic stiffness and damping coefficient generally follows a same trend. It is numerically shown that the critical speed of rotor-bearing is 3500 rpm.

Originality/value

The analytical solution provides a simple yet effective way to study the characteristics of surface textured bearings.

Details

Industrial Lubrication and Tribology, vol. 72 no. 9
Type: Research Article
ISSN: 0036-8792

Keywords

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Article

Amr M.I. Sweedan, Hothifa N. Rojob and Khaled M. El-Sawy

The purpose of this paper is to introduce a closed-form analytical solution to evaluate the nominal moment capacity and associated deflections of steel-FRP beam systems…

Abstract

Purpose

The purpose of this paper is to introduce a closed-form analytical solution to evaluate the nominal moment capacity and associated deflections of steel-FRP beam systems. The proposed solution takes into consideration the partial composite behavior resulting from the interfacial contact and slip between the subcomponents of the system.

Design/methodology/approach

The partial composite action theory was used to develop an elastic analytical solution for the deflection of simply supported composite steel-FRP beams subjected to a mid-span point load. The solution takes into consideration the partial composite behavior of the system that arises from the interlayer slip at the steel-FRP interface.

Findings

The developed analytical model is used to predict the nominal moment capacity of the composite beam and the load value at the onset of yielding in the steel subcomponent of the section. The distribution of shear forces induced in the steel fasteners due to the interfacial slip is also obtained analytically. A comparative study is conducted by comparing the analytical results to their counterparts resulting from finite element modeling of the composite steel-FRP system. The agreement between analytical results and finite element predictions validates the accuracy of the derived analytical solution for partial composite steel-FRP beams.

Research limitations/implications

The proposed solution applies only to the FRP strips and 6 mm steel bolts used in the study.

Originality/value

Recent studies revealed a promising efficiency of using mechanically fastened hybrid FRP sheets in strengthening steel beams. A major advantage of this technique is the ductile behavior of the steel-FRP system. The current paper introduces a closed-form analytical solution to evaluate the nominal moment capacity and associated deflections of steel-FRP beam systems. Forces developed at the steel-FRP interface due to the relative slip between both components are considered in the proposed analytical solution.

Details

International Journal of Structural Integrity, vol. 9 no. 5
Type: Research Article
ISSN: 1757-9864

Keywords

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Article

Y.C. LI

This paper presents approximate analytical solutions for the diffusion problems of a cylindrical hole in an infinite medium and a slot in an infinite medium with properly…

Abstract

This paper presents approximate analytical solutions for the diffusion problems of a cylindrical hole in an infinite medium and a slot in an infinite medium with properly prescribed boundary conditions and initial conditions. These solutions have much simpler forms than those of exact analytical solutions, and asymptotically approach the exact solutions with increasing time or the material point moving away from the internal boundary. The approximate analytical solution for the diffusion problem of a slot in an infinite medium is applied to establish a shape function for the infinite elements. Good agreement is found in comparison of our results with those presented by Li and Huang and Cinco‐Ley et al. Finally, an example simulating a primary recovery procedure in hydraulic fracturing technique for an oil field is presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

Matthew Montgomery and Sanford Fleeter

The first compressible flow solution based solely on the locallyanalytical method is developed. This is accomplished by developing the flowmodel and locally analytical

Abstract

The first compressible flow solution based solely on the locally analytical method is developed. This is accomplished by developing the flow model and locally analytical solution for inviscid subsonic compressible flow. The stream function for irrotational, compressible flow without body forces was chosen as the governing differential equation. To demonstrate the modelling and locally analytical solution, this analysis is then applied to predict the flow in convergent nozzles, both planar and axially symmetric, for different back pressures. Results are presented which demonstrate the effectiveness of this technique.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 1
Type: Research Article
ISSN: 0961-5539

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Article

Mei-Ling Wu and Jia-Shen Lan

The purpose of this study was to investigate the changes in solder joint stress when subjected to mechanical bending. The analytical theory pertaining to the stresses in…

Abstract

Purpose

The purpose of this study was to investigate the changes in solder joint stress when subjected to mechanical bending. The analytical theory pertaining to the stresses in the solder joint between the components (including the molding compound, the chip and the substrate) was described, and the printed circuit board (PCB) with a discontinuity function when the PCB assembly is subjected to mechanical bending was developed. Thus, the findings reported here may lead to a better understanding of the solder joint failure based on the Physics of Failure model.

Design/methodology/approach

This paper discusses the analytical model for calculating the stress in solder joints, as well as presents a simulation model that can be used for calculating the strain energy density of solder joint. First, the multilayer plate theory is used in discussing the composite material for the component, including the molding compound, the silicon chip and the substrate, or the PCB, including the copper layers, the fiber and the epoxy. Finally, the complete structure of the analytical model developed as a part of this current work is presented.

Findings

For the analytical model of multilayer structures in which the interconnection layer is discrete, mechanical bending has been modeled with respect to varying silicon chip length. The analytical model that describes the stress of the outermost solder joint experiences is chosen, as this is the typical solder joint failure. The analytical model can be applied to discrete solder joints, which are evaluated by calculating the matrix form. Owing to its use of the matrix equation, the analytical model can be highly combinatorial and thus more capable of calculating the solution.

Research limitations/implications

The analytical solution based on a simple concept was presented and validated using the finite element model for the stress experienced by solder joints subjected to mechanical bending. To verify that the simulation represents a real PCB case, the authors use the finite element method (FEM) to compare their case with the multilayer plate theory. Owing to the good agreement between the theory and simulation results, the authors conclude that the multilayer plate theory can be correctly applied in multilayer PCB and be used in an analytical model for the PCB assembly subjected to mechanical bending.

Practical implications

Owing to the good agreement between the theory and simulation results, the authors conclude that the multilayer plate theory can be correctly applied in multilayer PCB and be used in an analytical model for the PCB assembly subjected to mechanical bending.

Social implications

The analytical model is validated with the FEM model and provides the way to physically examine the solder joint failure mechanism. In this paper, the analytical model is developed as a means to assess the solder joint stress subjected to mechanical bending.

Originality/value

The analytical model treats the solder joint as discrete and has been successfully validated against the finite element model. The complete structure model (the second analytical model) is presented to discuss the effects of varying silicon chip length on the normal stress in solder joints. When the silicon chip length exceeds to 80 per cent of the total package length, the stress of the outermost solder joint increases rapidly. The design analysis findings have suggested that the failure of the outermost solder joint subjected to mechanical bending on the PCB assembly can be reduced by analyzing the analytical model.

Details

Soldering & Surface Mount Technology, vol. 29 no. 2
Type: Research Article
ISSN: 0954-0911

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Article

J.I. Ramos

The purpose of this paper is to develop a new transversal method of lines for one-dimensional reactiondiffusion equations that is conservative and provides piecewise…

Abstract

Purpose

The purpose of this paper is to develop a new transversal method of lines for one-dimensional reactiondiffusion equations that is conservative and provides piecewise–analytical solutions in space, analyze its truncation errors and linear stability, compare it with other finite-difference discretizations and assess the effects of the nonlinear diffusion coefficients, reaction rate terms and initial conditions on wave propagation and merging.

Design/methodology/approach

A conservative, transversal method of lines based on the discretization of time and piecewise analytical integration of the resulting two-point boundary-value problems subject to the continuity of the dependent variables and their fluxes at the control-volume boundaries, is presented. The method provides three-point finite difference expressions for the nodal values and continuous solutions in space, and its accuracy has been determined first analytically and then assessed in numerical experiments of reaction-diffusion problems, which exhibit interior and/or boundary layers.

Findings

The transversal method of lines presented here results in three-point finite difference equations for the nodal values, treats the diffusion terms implicitly and is unconditionally stable if the reaction terms are treated implicitly. The method is very accurate for problems with the interior and/or boundary layers. For a system of two nonlinearly-coupled, one-dimensional reactiondiffusion equations, the formation, propagation and merging of reactive fronts have been found to be strong function of the diffusion coefficients and reaction rates. For asymmetric ignition, it has been found that, after front merging, the temperature and concentration profiles are almost independent of the ignition conditions.

Originality/value

A new, conservative, transversal method of lines that treats the diffusion terms implicitly and provides piecewise exponential solutions in space without the need for interpolation is presented and applied to someone.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Ba-Phu Nguyen and Yun-Tae Kim

It is well known that the prefabricated vertical drain (PVD) installation process generates a significant soil disturbance around PVD. This disturbed zone significantly…

Abstract

Purpose

It is well known that the prefabricated vertical drain (PVD) installation process generates a significant soil disturbance around PVD. This disturbed zone significantly affects the rate of settlement and excess pore pressure dissipation. However, the characteristics of these zones were still uncertain and difficult to quantify; there remains large discrepancy among researchers. This study aims to develop a simple analytical solution for radial consolidation analysis of PVD-installed deposit considering mandrel-induced disturbance.

Design/methodology/approach

The proposed solution takes into account the nonlinear distributions of both horizontal hydraulic conductivity and compressibility toward the drain. The proposed solution was applied to analyze field behavior of test embankment in New South Wales, Australia.

Findings

Both effects significantly increased the time required to achieve a certain degree of consolidation. The effect of hydraulic conductivity on the consolidation rate was more significant than the effect of compressibility variation. And, the increased compressibility in the soil-disturbed zone due to mandrel installation significantly increased vertical strain of the PVD-improved soil deposit. The predicted results using the proposed analytical solution were in good agreement with the field measurements.

Practical implications

A geotechnical engineer could use the proposed analytical solution to predict consolidation behavior of drainage-installed ground.

Originality/value

Consolidation behavior of PVD-installed ground could be reasonably predicted by using the proposed solution with considering variations of both hydraulic conductivity and compressibility due to PVD installation.

Details

Engineering Computations, vol. 36 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article

Konrad Woronowicz, Majd Abdelqader, Ryszard Palka and Jordan Morelli

This paper aims to present a method for calculating electromagnetic fields, eddy currents and forces for a quasi-static two-dimensional (2-D) model of linear induction…

Abstract

Purpose

This paper aims to present a method for calculating electromagnetic fields, eddy currents and forces for a quasi-static two-dimensional (2-D) model of linear induction motors (LIMs) where the primary side is modeled as a collection of individual coils.

Design/methodology/approach

An analytical solution using Fourier series is derived for a general source with current excitations residing in an airgap and moving relative to a conducting plate and back iron. Ideal magnetic material with infinite permeability is used to model the primary iron above the primary source and the back iron below the conducting plate.

Findings

The analytical solution is compared to a commercial 2-D finite element analysis (FEA) simulation for validation and then compared to a 2-D FEA model with a more detailed geometry of the LIM. The analytical model accurately predicts LIM thrust even though the geometry of the primary core is simplified as an infinitely long flat slab. 2-D frequency FEA can be used successfully to predict in motion LIM performance.

Originality/value

The analytical solution presented here models the primary excitations as individual discrete coils instead of current sheets, which all existing models are based on. The discrete coils approach provides a more intuitive and realistic model of the LIM.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

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Article

Sima Samadpoor, Hadi Roohani Ghehsareh and Saeid Abbasbandy

The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity…

Abstract

Purpose

The purpose of this paper is to obtain semi-analytical solutions of similarity solutions for the nano boundary layer flows with Navier boundary condition. The similarity solutions of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are investigated.

Design/methodology/approach

In this work, the governing partial differential equations are transformed to a nonlinear ordinary differential equation by using some proper similarity transformations. Then an efficient semi-analytical method, the Laplace Adomian decomposition method (LADM) is applied to obtain semi-analytical solutions of the similarity solutions in both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface. To improve the accuracy and enlarges the convergence domain of the obtained results by the LADM, the study has combined it with Padé approximation.

Findings

Accuracy and efficiency of the presented method are illustrated and denoted through the tables and figures. Also the effects of the suction parameter λ and slip parameter K on the fluid velocity and on the tangential stress are investigated.

Originality/value

The similarity solutions of the governing partial differential equation are obtained analytically by using an efficient developed method, namely the Laplace Adomian decomposition-Padé method. The analytic solutions of nonlinear ordinary differential equation are constructed for both of viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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